Square and Square Root Functions: Let f and gbe defined byf(x) = x2 where x is any real

Chapter 1, Problem 7

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Square and Square Root Functions: Let f and gbe defined byf(x) = x2 where x is any real numberg(x) = where the values of x makeg(x) a real number a. Find f(g(3)), f(g(7)), g(f(5)), and g(f(8)).What do you notice in each case? Makea conjecture: For all values of x,f(g((x)) = , and g(f(x)) = .b. Test your conjecture by finding f(g( 9)) andg(f( 9)). Does your conjecture hold fornegative values of x?c. Plot f(x), g(x), and f(g(x)) on the samescreen. Use approximately equal scales onboth axes, as shown in Figure 1-4i. Explainwhy f(g(x)) = x, but only for nonnegativevalues of x.d. Deactivate f(g(x)), and plot f(x), g(x), andg(f(x)) on the same screen. Sketch the result.e. Explain why g(f(x)) = x for nonnegativevalues of x, but x (the opposite of x) fornegative values of x. What other familiarfunction has this property?